pcds (version 0.1.8)

edge.reg.triCM: The vertices of the \(CM\)-edge region in a triangle that contains the point

Description

Returns the edge whose region contains point, p, in the triangle tri\(=T(A,B,C)\) with edge regions based on center of mass \(CM=(A+B+C)/3\).

This function is related to rel.edge.triCM, but unlike rel.edge.triCM the related edges are given as vertices ABC for \(re=3\), as BCA for \(re=1\) and as CAB for \(re=2\) where edges are labeled as 3 for edge \(AB\), 1 for edge \(BC\), and 2 for edge \(AC\). The vertices are given one vertex in each row in the output, e.g., \(ABC\) is printed as rbind(A,B,C), where row 1 has the entries of vertex A, row 2 has the entries of vertex B, and row 3 has the entries of vertex C.

If the point, p, is not inside tri, then the function yields NA as output.

Edge region for BCA is the triangle \(T(B,C,CM)\), edge region CAB is \(T(A,C,CM)\), and edge region ABC is \(T(A,B,CM)\).

See also (ceyhan:Phd-thesis,ceyhan:comp-geo-2010,ceyhan:mcap2012;textualpcds).

Usage

edge.reg.triCM(p, tri)

Value

The \(CM\)-edge region that contains point, p in the triangle tri. The related edges are given as vertices ABC for \(re=3\), as BCA for \(re=1\) and as CAB for \(re=2\)

where edges are labeled as 3 for edge \(AB\), 1 for edge \(BC\), and 2 for edge \(AC\).

Arguments

p

A 2D point for which \(CM\)-edge region it resides in is to be determined in the triangle tri.

tri

A \(3 \times 2\) matrix with each row representing a vertex of the triangle.

Author

Elvan Ceyhan

References

See Also

rel.edge.tri, rel.edge.triCM, rel.edge.basic.triCM, rel.edge.basic.tri, rel.edge.std.triCM, and edge.reg.triCM

Examples

# \donttest{
A<-c(1,1); B<-c(2,0); C<-c(1.5,2);
Tr<-rbind(A,B,C);

P<-c(.4,.2)  #try also P<-as.numeric(runif.tri(1,Tr)$g)
edge.reg.triCM(P,Tr)

P<-c(1.8,.5)
edge.reg.triCM(P,Tr)

CM<-(A+B+C)/3
p1<-(A+B+CM)/3
p2<-(B+C+CM)/3
p3<-(A+C+CM)/3

Xlim<-range(Tr[,1])
Ylim<-range(Tr[,2])
xd<-Xlim[2]-Xlim[1]
yd<-Ylim[2]-Ylim[1]

plot(Tr,pch=".",xlab="",ylab="",axes=TRUE,xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05))
polygon(Tr)
L<-Tr; R<-matrix(rep(CM,3),ncol=2,byrow=TRUE)
segments(L[,1], L[,2], R[,1], R[,2], lty = 2)

txt<-rbind(Tr,CM,p1,p2,p3)
xc<-txt[,1]+c(-.02,.02,.02,-.05,0,0,0)
yc<-txt[,2]+c(.02,.02,.02,.02,0,0,0)
txt.str<-c("A","B","C","CM","re=T(A,B,CM)","re=T(B,C,CM)","re=T(A,C,CM)")
text(xc,yc,txt.str)
# }